Multistability and its Annihilation in the Chua’s Oscillator with Piecewise-Linear Nonlinearity

Abstract

This contribution uncovers numerical evidence of hysteric dynamical behaviors for the same set of the circuit parameters of the Chua’s circuit with traditional piecewise-linear nonlinearity. Stationary points and the symmetry property of the model first forecast the possible evidence of coexisting attractors. Then, well known nonlinear analysis approach based on the bifurcation diagrams, two-parameter diagrams, phase portraits, two parameter Lyapunov exponent diagrams, graph of maximum Lyapunov exponents, and attraction basins are exploited to characterize the dynamical behavior of the oscillator including coexisting orbits. Finally, the simultaneous existence of both periodic and chaotic orbits highlighted in the Chua’s oscillator is also annihilated based on linear controller. Numerical findings indicate control method ’s efficacy by combining two periodic routes and one chaotic route with another chaotic route.

Keywords

• Chua’s oscillator
• Chaotic systems
• piecewise-linear nonlinearity
• Multistability control
• merging crisis

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